Chi Square Table

 

The chi-squared (I) test is used to determine whether there is a significant difference between the expected frequencies and the observed frequencies in one or more categories according to a specific hypothesis (e.g. H0: Variables A and B are independent   H1: Variable A and B are dependent

Pearson’s Chi-square test statistic is computed from the formula below:

Chisquare formulaWhere, α is the level of significance, d.f is the degree of freedom

P-Values

df0.9950.990.9750.950.90.10.050.0250.010.005
1000.0010.0040.0162.7063.8415.0246.6357.879
20.010.020.0510.1030.2114.6055.9917.3789.2110.597
30.0720.1150.2160.3520.5846.2517.8159.34811.34512.838
40.2070.2970.4840.7111.0647.7799.48811.14313.27714.86
50.4120.5540.8311.1451.619.23611.0712.83315.08616.75
60.6760.8721.2371.6352.20410.64512.59214.44916.81218.548
70.9891.2391.692.1672.83312.01714.06716.01318.47520.278
81.3441.6462.182.7333.4913.36215.50717.53520.0921.955
91.7352.0882.73.3254.16814.68416.91919.02321.66623.589
102.1562.5583.2473.944.86515.98918.30720.48323.20925.188
112.6033.0533.8164.5755.57817.27519.67521.9224.72526.757
123.0743.5714.4045.2266.30418.54921.02623.33726.21728.3
133.5654.1075.0095.8927.04219.81222.36224.73627.68829.819
144.0754.665.6296.5717.7921.06423.68526.11929.14131.319
154.6015.2296.2627.2618.54722.30724.99627.48830.57832.801
165.1425.8126.9087.9629.31223.54226.29628.8453234.267
175.6976.4087.5648.67210.08524.76927.58730.19133.40935.718
186.2657.0158.2319.3910.86525.98928.86931.52634.80537.156
196.8447.6338.90710.11711.65127.20430.14432.85236.19138.582
207.4348.269.59110.85112.44328.41231.4134.1737.56639.997
218.0348.89710.28311.59113.2429.61532.67135.47938.93241.401
228.6439.54210.98212.33814.04130.81333.92436.78140.28942.796
239.2610.19611.68913.09114.84832.00735.17238.07641.63844.181
249.88610.85612.40113.84815.65933.19636.41539.36442.9845.559
2510.5211.52413.1214.61116.47334.38237.65240.64644.31446.928
2611.1612.19813.84415.37917.29235.56338.88541.92345.64248.29
2711.80812.87914.57316.15118.11436.74140.11343.19546.96349.645
2812.46113.56515.30816.92818.93937.91641.33744.46148.27850.993
2913.12114.25616.04717.70819.76839.08742.55745.72249.58852.336
3013.78714.95316.79118.49320.59940.25643.77346.97950.89253.672
4020.70722.16424.43326.50929.05151.80555.75859.34263.69166.766
5027.99129.70732.35734.76437.68963.16967.50571.4276.15479.49
6035.53437.48540.48243.18846.45974.39779.08283.29888.37991.952
7043.27545.44248.75851.73955.32985.52790.53195.023100.425104.215
8051.19253.5457.15360.39164.27896.578101.879106.629112.329116.321
9059.19661.75465.64769.12673.291107.565113.145118.136124.116128.294
10067.32870.06574.22277.92982.358118.498124.342129.561135.807140.169

The P value or calculated probability is the estimated probability of rejecting the null hypothesis (H0) of a study question when that hypothesis is true.

Interpretation of P-Values

Assuming P-Value is 0.04, this implies that there is moderately strong evidence that the null hypothesis does not hold

NB:

  • When P-values start being less than 0.05 chances that the null hypothesis will not hold becomes extremely high hence Unlikelihood of a true null.
  • When P-Values become greater than 0.05 chances that the null hypothesis will not hold becomes extremely low, hence likelihood of a true null

Below is a more detailed interpretation of P-Value:

Table 1: P-Values and its comments/ Interpretation

P-ValuesComment
Over 0.1No evidence that the null hypothesis does not hold
0.05 – 0.1Very weak evidence that the null hypothesis does not hold.
0.01 – 0.05Moderately strong evidence that the null hypothesis does not hold
Under 0.01Strong evidence that the null hypothesis does not hold

H0: independent   H1: dependent

Caution!!:

P-values deal with only and only a question of how likely you data is to be, with the assumption of a true null hypothesis (independence)? It does not, I repeat, it DOES NOT measure support for the alternative hypothesis (i.e. dependence) neither does it measure the level of statistical significances-Why? Answers to this and more will be discussed further in the next edition. Therefore due to this limitation, we’ll be covering the very common misinterpretation of P-Values in our forthcoming edition.

 

 

 

 

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